The Mixtups had the concept of a Great Year, which was around 5 of our years. This had 20 seasons, usually of 91 days, the names of which were the names of the 7 days, followed by the names of the 13 weeks, making 20 in all. Serpent seasons however had 14 weeks rather than 13, though otherwise following the normal progression of days and weeks; the 'leap week' was omitted every 8th Great Year which was not also a multiple of 80 such Years, such seasons being known as 'short Serpents'. A new Era started whenever the Day of the Sun in the Week of the Rabbit, in the Season of the Sun, coincided with New Year's Day. The years of an Era were more prosaically numbered 1,2,3,4,..etc.

An archaeologist asks you to examine a sculpture with the Mixtup inscription:

'Finished by Broltzlan on New Year's Day, Era 50, Year 47, Day of the Sun, Week of Fire, Season of the Earth.'

The full cycle of 80 Great Years has 10*14609 + 7 = 146097 days for this 400 Gregorian-year cycle, for an average year length of 365.2425 days--the same as the average Gregorian year.

Year 47 of an Era was preceded by 46 years, or 5 cycles of 8 years plus 6 more years: 5*14609 + 6*1827 = 84007 days, or 12001 weeks. If the leap weeks do not interrupt the cycle of week names (i.e., do not necessarily start with week of the Rabbit), the previous year ended on a week of the Earth and the New Year on a week of Dog, rather than Fire as the native stated. And of course if the leap week goes nameless and the new year begins with season Sun, then he's also lying.

In New Year's Day refers to the Great Year rather than seasonal year, it should be the Season of the Sun, rather than Earth. However, if they have New Year's Day every four seasons, then the third seasonal year of the 47th Great year could begin with a Season Earth, but since an integral number of weeks occurred from the beginning of the GY, it would still be the week of the Dog.

This turned out more complex than I thought it would, and hopefully I didn't err somewhere. It was especially hard considering seasonal years vs Great Years.

But it does lead to a riddle: If the natives drink champaigne on Great New Year's Day, what alcoholic beverage do they consume on the completion of four seasons (a seasonal year)?